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How to Compute the Mean Particle Diameter from a LISST Volume Distribution

How to Compute the Mean Particle Diameter from a LISST Volume Distribution

[Sequoia, March 26, 2010]

In the table below, the computation of the mean particle size from a LISST volume distribution is outlined.Column A is the size class number, from 1-32.
Column B is the MID POINT of the size bin in µm. In this example we are using the size classes associated with a LISST type B randomly shaped inversion (LISST Bin Sizes).
Column C is the Volume Distribution in µl/l.Each row in column D (dSum) is computed as the size class # for that row multiplied with the volume concentration in the size class. For example, for size class 8, dSum is equal to 8 * 3.035 = 24.28.

A

B

C

D

Size class

Size class mid point (µm)

Volume Distribution (µl l-1)

dSum
(Size class # * VC in size class)

1

1.09

0.190

0.190

2

1.28

0.256

0.512

3

1.51

0.360

1.080

4

1.79

0.616

2.464

5

2.11

0.853

4.265

6

2.49

1.041

6.246

7

2.93

1.429

10.003

8

3.46

3.035

24.280

9

4.09

4.071

36.639

10

4.82

4.419

44.190

11

5.69

4.818

52.998

12

6.71

5.714

68.568

13

7.92

6.218

80.834

14

9.35

6.252

87.528

15

11.03

6.151

92.265

16

13.02

6.360

101.76

17

15.36

6.288

106.896

18

18.13

6.311

113.598

19

21.39

6.732

127.908

20

25.25

7.726

154.52

21

29.79

8.252

173.292

22

35.16

9.573

210.606

23

41.49

10.666

245.318

24

48.96

11.581

277.944

25

57.77

11.843

296.075

26

68.18

12.214

317.564

27

80.45

11.177

301.779

28

94.94

9.434

264.152

29

112.04

6.993

202.797

30

132.21

4.750

142.500

31

156.02

3.128

96.968

32

184.11

2.300

73.600

VD = VC

dSum

180.751

3719.339

By definition, the mean particle size in terms of size class number is now dSum/VD = dSum/VC, in this example 3719.339 / 180.751 = 20.57714.

We can now see that the mean particle size, in terms of size class numbers is somewhere between size class 20 and 21, i.e. somewhere between 25.25 and 29.79 µm.

Now round down dSum/VC to the nearest integer, in this case it would be 20.

Compute the remainder; in this case it would be 20.57714 – 20 = 0.57714.

The mean particle size is now computed as the midpoint of size class 20 (from rounding down dSum/VC) multiplied by the ratio of the bin midpoints (200^(1/32) = 1.1801) raised to the power of the remainder: 25.25 * 1.1801^0.57714 = 27.78µm.